Consider the implication to be some claim, for example, “When it’s raining (A), it’s wet (B)”. The value of the implication tells us whether we should call the claimant a liar or. So in case it’s raining (A = true) and is is not wet (B = false) the claim turns out to be false, so the value of the implication is false.

Now, supposing it is not raining (A = false). It doesn’t matter whether it’s wet or not, we can’t call the claim false because there just isn’t enough information.

It’s about falsifiability (or lack thereof, in case A is never true).